When handling or processing multiple documents, such as banknotes (e.g., currency or paper money), checks, legal-related documents, and other document types, it is sometimes convenient or desirable to bundle the documents into batches. For example, document straps may be used to bundle banknotes having the same denomination or other attributes into bundles having a predetermined number of banknotes. Such bundling of documents may occur in many different applications, including the sorting, authentication, counting, creation, or other processing of currency. Current systems may fail to properly, snugly, or efficiently wrap document straps around stacks of documents. For example, when applying a document strap to a stack of documents, current systems may apply a document strap too loosely, causing the stack of documents to be improperly secured or vulnerable to documents falling out of the bundle. Indeed, current strapping systems or methods may suffer from other issues or drawbacks as well.